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The length of arc PQR
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21 Dec 2022, 02:01
21 Dec 2022, 02:01
Expert Reply
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Question Stats:
44% (01:24) correct
55% (01:12) wrong based on 43 sessions
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GRE The length of arc PQR.jpg [ 26.3 KiB | Viewed 3045 times ]
Point O is the center of the circle.
Quantity A |
Quantity B |
The length of arc PQR |
\(3\pi\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: The length of arc PQR
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23 Dec 2022, 05:00
23 Dec 2022, 05:00
Expert Reply
One side of the triangle oR is labeled as 2. Therefore, the \(C=2 \pi 2=4 \pi\)
If the angle is 60° that means the area of the circle OUTSIDE of the triangle is 5/6 of C
\(\frac{5}{6} * 4 \pi\)
\(\frac{20}{6} \pi = \frac{10}{3} \pi \)
\(\frac{10}{3} \pi > 3 \pi\)
If the angle is 60° that means the area of the circle OUTSIDE of the triangle is 5/6 of C
\(\frac{5}{6} * 4 \pi\)
\(\frac{20}{6} \pi = \frac{10}{3} \pi \)
\(\frac{10}{3} \pi > 3 \pi\)
The length of arc PQR
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30 Jan 2024, 20:07
30 Jan 2024, 20:07
\(\dfrac{Length of Arc PR}{Circumference of the Circle} = \dfrac{Angle of Arc}{Angle of Circumference} = \dfrac{60}{360} = \dfrac{1}{6}\)
The Length of Arc PR is \(\dfrac{1}{6}^{th}\) of Circumference of Circle
The Length of Arc PQR = \(1-\dfrac{1}{6} = \dfrac{5}{6}^{th}\) of Circumference of Circle
Since Circumference of the Circle is \(2 \pi r\)
Length of Arc PQR \(= 2 \pi r \times \dfrac{5}{6} = \dfrac{5 \pi r}{3}\)
Since \(r=2\) (given)
Length of Arc PQR \(= \dfrac{5 \pi 2}{3} = \dfrac{10 \pi}{3}\)
Now
\(\dfrac{10 \pi}{3} > 3 \pi\)
\(3.333 \pi > 3 \pi\)
Quantity A is the greatest.
The Length of Arc PR is \(\dfrac{1}{6}^{th}\) of Circumference of Circle
The Length of Arc PQR = \(1-\dfrac{1}{6} = \dfrac{5}{6}^{th}\) of Circumference of Circle
Since Circumference of the Circle is \(2 \pi r\)
Length of Arc PQR \(= 2 \pi r \times \dfrac{5}{6} = \dfrac{5 \pi r}{3}\)
Since \(r=2\) (given)
Length of Arc PQR \(= \dfrac{5 \pi 2}{3} = \dfrac{10 \pi}{3}\)
Now
\(\dfrac{10 \pi}{3} > 3 \pi\)
\(3.333 \pi > 3 \pi\)
Quantity A is the greatest.
